What numbers would you need to make a life changing decision?

I want to explore a sensitive matter about a real person who’s discovered that he has cancer. I hope that I’m using this to illustrate an important point about the human capacity to interpret risk, but hope I don’t lose sight of the humanity of this situation.

On the 13th March 2018, the journalist and environmental campaigner George Monbiot announced that he had prostate cancer and that he’d be undergoing serious surgery to deal with it. I personally believe everyone should read the article, it’s brilliant, poignant personal journalism. I especially believe anyone working in big data/ learning analytics for this extract:

“I was offered a choice: radical surgery or brachytherapy. This means implanting radioactive seeds in the parts of the prostate affected by cancer. Brachytherapy has fewer side effects, and recovery is much faster. But there’s a catch. If it fails to eliminate the cancer, there’s nothing more that can be done. This treatment sticks the prostate gland to the bowel and bladder, making surgery extremely difficult. Once you’ve had one dose of radiation, they won’t give you another. I was told that the chances of brachytherapy working in my case were between 70 and 80%. The odds were worse, in other words, than playing Russian roulette (which, with one bullet in a six-chambered revolver, gives you 83%). Though I have a tendency to embrace risk, this was not an attractive option.”

What a choice. One treatment that risks impotence or bladder problems for life, one that will probably work, but if it doesn’t work seriously curtails future options for treatment. I’ve been dwelling on the 70 – 80%. You’d bet on that right?

On a life-changing decision?

I’ve recently come across this diagram about what meaning people put on to perceptions of probability (thanks to @simongerman600). It’s interesting that according to this analysis that if people were told that something was 70-80% likely to work most people would use a range of words including ‘probably’, ‘we believe’, ‘likely’, ‘probable’, ‘very good chance’ or even ‘highly likely’. That’s actually an enormous range for a 10% difference.

What a difference. ‘Probably’ to ‘highly likely’. I can’t help but feel that these words reflect more on the person looking at the data than the data itself. As a naturally glass-half-empty kind of guy, I think I’d be using ‘probably’. I wonder if the optimists in my life would use ‘highly likely’.

Monbiot adds another important insight into scales.

“When you are diagnosed with prostate cancer, your condition is ranked on the Gleason Score, which measures its level of aggression. Mine is graded at seven out of 10. But this doesn’t tell me where I stand in general. I needed another index to assess the severity of my condition, so I invented one: the Shitstorm Scale. How does my situation compare to those of people I know, who contend with other medical problems or family tragedies? How does it compare to what might have been, had the cancer not been caught while it was still – apparently – confined to the prostate gland? How does it compare to innumerable other disasters that could have befallen me?”